Dave;
Brining does wonders to certain meats, especially to fish, poulty and pork....not so effective on red meats like beef, lamb, etc., at least IMHO.
I have brined a cooler full of butts overnight, but have some issues brining a whole butt. Since a butt is a thick mass of meat with not much way to get to the interior tissue, the brine really only is partially effective. A turkey is hollow so the brine can work into the cavity....a butt is a challenge.
So.....consider injecting your brine instead. I use a spitjack, but any needle large enough to pass spices will work. Do deep tissue injections while the butt is in a large 2 gallon zip lock type baggie. Pump plenty into the meat since lots of it will ooze out. The brine that comes out will continue to brine the meat while it rests.
I pour the rest of the brine into the bag to submerge, then store in fridge overnight.
Choose any brine or injection recipe you wish just remember it needs to pass thru the needle.
As long as it has liquid, sugar and salt....it will work.
Injecting is brining, just an internal method of application.